LING 438/538 Computational Linguistics Sandiway Fong Lecture 6: 9/7.
LING 6932 Topics in Computational Linguistics
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Transcript of LING 6932 Topics in Computational Linguistics
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LING 6932 Topics in Computational Linguistics
Hana FilipLecture 2: Regular Expressions, Finite State Automata
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Regular expressions
formulas for specifying text stringsHow can we search for any of these strings?
woodchuckwoodchucksWoodchuckWoodchucks
Figure from Dorr/Monz slides
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Regular Expressions
Basic patterns of regular expressionsPerl-based syntax (slightly different from other notations for regular expressions as used in UNIX, for example)/Woodchuck/ matches any string containing the substring Woodchuck, if your search application returns entire lines, for example‘/’ notation used by Perl, NOT part of the RE
Google: Woodchuck Draft CiderProducers of Woodchuck Draft Cider in Spingfield, VT.www.woodchuck.com/ - 17k - Cached - Similar pages
Slide from Dorr/Monz
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Regular Expressions
Regular expressions are CASE SENSITIVEThe pattern /woodchuck/ will not match the string WoodchuckDisjunction /[wW]oodchuck/
Slide from Dorr/Monz
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Regular Expressions
Ranges [A-Z]
Slide from Dorr/Monz
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Regular Expressions
Negation /[^a]/ ^: caret
‘match any single character except a’
Slide from Dorr/Monz
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Regular Expressions
Operators ? , * and +? (0 or 1)
/woodchucks?/ woodchuck or woodchucks/colou?r/ color or colour
* (0 or more)/oo*h!/ oh! or ooh! or ooooh!
+ (1 or more)
• /o+h!/ oh! or ooh! or ooooh!
related to the immediately preceding character or regular expression
*+
Stephen Cole Kleene Wild card ./beg.n/ begin or began or begun
any character between beg and n (except a carriage return)
Slide from Dorr/Monz
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Regular Expressions
Anchors ^ and $ start of line
/^[A-Z]/ “Ramallah, Palestine”
/^[^A-Z]/ “¿verdad?” “really?”
end of line
/\.$/ “It is over.”
/.$/ ?
Boundaries \b and \B/\bon\b/ “on my way” “Monday” (boundary)
/\Bon\b/ “automaton” (non-boundary)
Slide from Dorr/Monz
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Disjunction, Grouping, Precedence
Disjunction |
/yours|mine/ “it is either yours or mine”
/gupp(y|ies)/ “guppy” or “guppies”
Column 1 Column 2 Column 3 …How do we express this?/Column[0-9]*/ ‘space’ /(Column[0-9]*)*/ NOT a RE character
matches the word Column, followed by one number, followed by zero or more spaces, the whole pattern repeated any number of times (zero or more times)
Slide from Dorr/Monz
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Disjunction, Grouping, Precedence
Operator Precedence HierarchyParenthesis ()Counters * + ? Sequences and anchors the ^my end$Disjunction |
REs are greedy!They always match the largest string they can
Slide from Dorr/Monz
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Example
Find me all instances of the word “the” in a text.
/the/Misses capitalized examples
/[tT]he/Returns “other” or “theology”
/\b[tT]he\b/ matches “the” or “The”
/[^a-zA-Z][tT]he[^a-zA-Z]/
/(^|[^a-zA-Z])[tT]he[^a-zA-Z]/Matches “the_” or “the25”
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Errors
The process we just went through was based on two fixing kinds of errors
Not matching things that we should have matched (The)
– False negatives
Matching strings that we should not have matched (there, then, other)
– False positives
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Errors cont.
We’ll be telling the same story for many tasksReducing the error rate for an application often involves two antagonistic efforts:
Increasing accuracy (minimizing false positives)Increasing coverage (minimizing false negatives).
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More complex RE example
Regular expressions for prices/$[0-9]+/
Doesn’t deal with fractions of dollars
/$[0-9]+\.[0-9][0-9]/Doesn’t allow $199, not at a word boundary
/\b$[0-9]+(\.[0-9]0-9])?\b)/
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Advanced operators
Regular expression operators for counting
RE Match
{n} exactly n occurrences of the previous character or expression
{n,m} from n to m occurrences of the previous character or expression
{n, } at least n occurrences of the previous character or expression
/a\.{24}z/ a followed by 24 dots followed by z
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Advanced operators
To refer to characters that are special themselves precede them with a backslash
RE Match Example Strings Matched
\* an asterisk “*” “K*A*P*L*A*N”
\. a period “.” “Dr.Livingston, I presume.”
\? A question mark “?” “Would you light my candle?”
\n a newline
\t tab
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Advanced operators
Slide from Dorr/Monz
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Substitutions and Memory
Substitution operator s/regexp1/regexp2/ (UNIX, Perl)
s/colour/color/s/colour/color/g
Substitute as many times as possible!
Case insensitive matching
s/colour/color/i
Slide from Dorr/Monz
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Substitutions and Memory
Substitutions“the Xer they were, the Xer they will be”constrain the two X’s to be the same string
/the (.*)er they were, the $1er they will be/
/the (.*)er they (.*), the $1er they $2/
Using numbered memories or registers: $1, $2, etc. used to refer back to matches
An extended feature of regular expressions
Slide from Dorr/Monz
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Eliza [Weizenbaum, 1966]
User: Men are all alikeELIZA: IN WHAT WAYUser: They’re always bugging us about something or otherELIZA: CAN YOU THINK OF A SPECIFIC EXAMPLE?User: Well, my boyfriend made me come hereELIZA: YOUR BOYFRIEND MADE YOU COME HEREUser: He says I’m depressed much of the timeELIZA: I AM SORRY TO HEAR THAT YOU ARE DEPRESSED
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Eliza-style regular expressions
s/.* YOU ARE (depressed|sad) .*/I AM SORRY TO HEAR YOU ARE \1/s/.* YOU ARE (depressed|sad) .*/WHY DO YOU THINK YOU ARE \1/s/.* all .*/IN WHAT WAY/s/.* always .*/CAN YOU THINK OF A SPECIFIC EXAMPLE/
Step 1: replace first person with second person references
s/\bI(’m | am)\b /YOU ARE/g
s/\bmy\b /YOUR/g
S/\bmine\b /YOURS/g
Step 2: use substitutions that look for relevant patterns in the input and create an appropriate output (reply)
Step 3: use scores to rank possible transformations
Slide from Dorr/Monz
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Summary on REs so far
Regular expressions are perhaps the single most useful tool for text manipulation
Dumb but ubiquitous
Eliza: you can do a lot with simple regular-expression substitutions
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Three Views
Three equivalent formal ways to look at what we’re up to (thanks to Martin Kay)
Regular Expressions
Regular LanguagesFinite State Automata
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Finite State Automata
Terminology: Finite State Automata, Finite State Machines, FSA, Finite AutomataRegular expressions are one way of specifying the structure of finite-state automata.FSAs and their close relatives are at the core of most algorithms for speech and language processing.
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Finite-state Automata (Machines)
/^baa+!$/
q0 q1 q2 q3 q4
b a a !
a
state transitionfinalstate
baa! baaa! baaaa! baaaaa! ...
Slide from Dorr/Monz
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Sheep FSA
We can say the following things about this machineIt has 5 statesAt least b, a, and ! are in its alphabetq0 is the start stateq4 is the final (= accept) stateIt has 5 transitions
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More Formally: Defining an FSA
You can specify an FSA by enumerating the following things.
a finite set of states: Q
a finite alphabet of symbols: the start state: q0
The set of accepting/final states: F such that FQ
A transition function (q,i) that maps Qx to Q
Given a state qQ and an input symbol i, (q,i) returns a new state q’Q.
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Yet Another View
State-transition table
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Recognition
Recognition is the process of determining if a string should be accepted by a machineOr… it’s the process of determining if a string is in the language we’re defining with the machineOr… it’s the process of determining if a regular expression matches a string
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Recognition
Traditionally, (Turing’s idea, 1936) this process is depicted with a tape.
http://www.cs.princeton.edu/introcs/75turing/
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Recognition - Execution
Start in the start stateExamine the current input in the active cellConsult the table: a finite table of instructions (a state transition diagram) that specifies exactly what action the machine takes at each stepGo to a new state and update the tape pointer.Until you run out of tape.
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Input Tape
b a a a
q0 q1 q2 q3 q3 q4
!
0 1 2 3 4
b a a !a
ACCEPT
Slide from Dorr/Monz
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Input Tape
a b a ! b
q0
0 1 2 3 4
b a a !a
REJECT
Slide from Dorr/Monz
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Adding a failing state
q0 q1 q2 q3 q4
b a a !
a
qFa
!
b
! b ! b
b
a
!
Slide from Dorr/Monz
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Tracing D-Recognize
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Key Points
Deterministic means that at each point in processing there is always one unique thing to do (no choices).D-recognize is a simple table-driven interpreterThe algorithm is universal for all unambiguous languages.To change the machine, you change the table.
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Key Points
Deterministic Pattern Example: Consider a set of traffic lights; the sequence of lights is red - red/amber - green - amber - red. The sequence can be pictured as a state machine, where the different states of the traffic lights follow each other.
Each state is dependent solely on the previous state, so if the lights are green, an amber light will always follow - that is, the system is deterministic. Deterministic systems are relatively easy to understand and analyse, once the transitions are fully known.
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Key Points
Crudely therefore… matching strings with regular expressions (a la Perl) is a matter of
translating the expression into a machine (table) and passing the table to an interpreter
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Recognition as Search
You can view this algorithm as state-space search.States are pairings of tape positions and state numbers.Operators are compiled into the tableGoal state is a pairing with the end of tape position and a final accept state
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Generative Formalisms
A formal Language is a model m which can both generate and recognize all and only the strings of a formal language; each string is composed of symbols from a finite set of symbols (alphabet)
L(m) ‘a formal language L characterized by the model m’Finite-state automata define formal languages (without having to enumerate all the strings in the language)The term Generative is based on the view that you can run the machine as a generator to get strings from the language.
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Generative Formalisms
FSAs can be viewed from two perspectives:Acceptors that can tell you if a string is in the language (recognition)Generators to produce all and only the strings in the language (production)
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Summary
Regular expressions are just a compact textual representation of FSAsRecognition is the process of determining if a string/input is in the language defined by some machine.
Recognition is straightforward with deterministic machines.